Cayley树上的Heisenberg反铁磁体：低能谱和奇偶位不平衡
Heisenberg antiferromagnet on Cayley trees: low-energy spectrum and even/odd site imbalance
摘要：
为了理解局域亚晶格不平衡在s=1/2量子反铁磁体低能谱中的作用，我们在配位3 Cayley树上研究了s=1/2量子最近邻海森堡反铁磁体.我们使用密度矩阵重整化群（DMRG）技术的通用树图的实现进行多体计算。我们发现键心Cayley树有一个准生成集的一个低洼的状态塔和一个“反常”的单重-三重有限尺寸的间隙标度。为了理解从多体基态到第一激发态的结构，我们考虑了由单模近似给出的波函数，它与DMRG波函数有很高的重叠。通过对基态纠缠谱的观测，我们得到了一幅低能自由度是由亚晶格不平衡引起的“巨自旋”的图像，这有助于我们从分析上理解有限尺寸自旋隙的标度。本文将Schwinger-boson平均场论推广到非均匀晶格中，发现了平均场参数在空间上不均匀的基态。
英文摘要：
To understand the role of local sublattice imbalance in low-energy spectra of s=1/2 quantum antiferromagnets, we study the s=1/2 quantum nearest neighbor Heisenberg antiferromagnet on the coordination 3 Cayley tree. We perform many-body calculations using an implementation of the density matrix renormalization group (DMRG) technique for generic tree graphs. We discover that the bond-centered Cayley tree has a quasidegenerate set of a low-lying tower of states and an "anomalous" singlet-triplet finite-size gap scaling. For understanding the construction of the first excited state from the many-body ground state, we consider a wave function ansatz given by the single-mode approximation, which yields a high overlap with the DMRG wave function. Observing the ground-state entanglement spectrum leads us to a picture of the low-energy degrees of freedom being "giant spins" arising out of sublattice imbalance, which helps us analytically understand the scaling of the finite-size spin gap. The Schwinger-boson mean-field theory has been generalized to nonuniform lattices, and ground states have been found which are spatially inhomogeneous in the mean-field parameters.
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